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Let's say I have to get the composite of a relation: R composite of R.

What if the elements in that composite repeat? Should I say it twice?

Example: R is a relation.

R= { (1,1), (1,2), (1,3), (2,3), (2,4), (3,1), (5,4) }

R^2= R composite R= {(1,1), (3,1), (1,2), (3,2), (1,3), (3,3), (1,3), (1,4), (1,1), (2,1)}

Note (1,3), (1,1) comes up twice

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  • $\begingroup$ What does that mean? Do you have an example in mind? $\endgroup$ Dec 10 '14 at 0:55
  • $\begingroup$ I'll edit it in. $\endgroup$ Dec 10 '14 at 0:55
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Note that $R^2$ is, at its most basic, a set. Therefore, for instance, $\{(1,1)\}$ is the same as $\{(1,1),(1,1)\}$. By convention, we usually only write elements in a set once, but it doesn't actually matter.

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  • $\begingroup$ So if I put (1,1) in 4 times, it would be equivalent to it being there once? $\endgroup$ Dec 10 '14 at 1:01
  • $\begingroup$ @munchschair: Yep! $\endgroup$ Dec 10 '14 at 1:02

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